This has been my experience.

I was in a survival class a few years ago where we did this for real. The air temp was about 45 degF, and it was breezy. I don't know what the lake water temp was but it felt cold. Wearing what we would normally wear for a dayhike in those temps, we did this drill:

1) Walk out to the end of a 100' dock on the lake

2) Jump in the water fully clothed and swim to shore

3) Wait a few minutes while standing in the breeze

4) Remove clothes, wring them out & put them back on (no George Constanza jokes allowed!)

5) Put on our emergency plastic bags (cutting a face hole in one corner and wearing it like a poncho)

6) Put our hands in a bucket of icewater (with ice cubes!) and hold them in for 1 minute

7) Jog over to another area and start a fire with the gear in our pockets

I recall that by the time I was sparking my fire, my long underwear and Patagonia fleece jacket were only damp and they felt very comfortably warm. It took longer for my thin Ex Officio nylon pants to dry but since I had a fire going by then it was OK.

However I've not tried this drill with cotton clothing. So in that case it might be best to ditch it, I'm not sure.

BTW in this drill I learned that the container I used for my Spark-Lite was not really waterproof and the Spark-Lite wouldn't work. The REI Storm matches saved the day. The vaseline cotton balls worked great.